Given that Intel made that exact move with Altera a while ago, this is yet another simple reason why AMD would do just the same. AMD is a direct Intel competitor, and as such, they have little choice but expand their offering in the same way, otherwise they're bound to lose ground one way or another in the long run. This is pretty common in the industry. Major competitors tend to expand their offerings in the same way. Just my 2 cents.
Intel bought Altera as part of their effort to fill their foundries and provide foundry services. AMD has no such incentive to do the same with Xilinx since they divested their foundries to GlobalFoundries and now use TSMC.
If Intel had a plan for CPU compatible FPGAs, it has not worked out.
I think you are strictly seeing it from a technical POV. And you seem to consider Intel strictly as a CPU vendor (with foundry services) not willing or able to expand their horizons. Intel already does more than just design and sell CPUS. Filling their foundries may have been an incentive, but the end result is much more than just that.
From a business POV, buying Altera means Intel is now also an FPGA vendor (with a significant market). The fact they would mix FPGA and CPU technologies could be interesting, but is almost irrelevant at this point. That means, at this point, that Intel has a bigger market share overall as a company. All big companies need to expand in that way in order to survive long term. Diversification is key.
Now regarding mixing technologies, that's probably not for tomorrow, but there could be some interesting opportunities. Intel is not ARM. I don't see - and don't think that would make sense - them, for instance, embedding one of their CPU cores in FPGAs, the way it has already happened with ARM cores. I doubt that would fit Intel's strategy or model. But I could imagine something similar, but IMO more appropriate for Intel's strategy: embedding some tightly-coupled FPGA in their future CPUs, to be used as reconfigurable accelerators for instance. The difference may seem subtle, except that this way they would sell powerful CPUs with some integrated FPGA fabric, and not FPGAs with some integrated and only modest CPU core.